Sure but unless it's cheaper than the current, 10 minute slower trains (which it won't be). Why would people use it? Services won't get cut if demand it still there and it's a different operator.
Like i said, China is losing **** loads of money on their HS trains. Nowhere near enough people are using them.
HS2 moves many of the long distance commuters who are going from the ends of the line to the new line, meanwhile the commuters using the old line for a short hop between the end points now have more space because people are using the other option.
This is really simple stuff.
It's not speed, it's about increasing the capacity, for both the long distance travel, and for local capacity by completely separating them. Adding a new set of tracks is the only possible way to do that for many of our rail routes, as we're frequently using the same routes that were bult 100 years ago and have in many cases went way past the design capacity decades ago (IIRC they've tried bodging it with longer trains with more carriages which involved massive works on the stations, fiddling with the train seating to squeeze more in etc)
I have to use a route that includes a "commuter" section at times and I absolutely hate it, because much of the time there is zero seating and it's crammed to the point where Sardines would be organising a strike, for a 2-3 hour trip about an hour or so involves stopping every 5 minutes to have more people get on.
Trains along any reasonably popular commuter route are actively unpleasant, and positively hellish if you're going a long way and have to endure those sections.
I don't care if the train is 10 minutes faster, I care that something like HS2 means that they increase capacity by splitting the types of traffic across two physical lines which means that there is space to actually get on the train without the need of a bullzozer pushing me in the door,. Let alone the fact that I'm likely to be able to find a seat so I don't spend 2 hours standing. For a lot of people doing that sort of distance on a regular basis one of the reasons you go by train is the hope you can do some work whilst travelling, you can't do that whilst standing with barely room to pull your phone out.
This is what HS2 does, it gives that extra capacity to both let existing passengers travel in a little more comfort, but adds a ton more capacity as you've doubled the actual physical capability of the route so can now run many more trains both local and long distance.
Also you can't necessarily compare China to the UK, IIRC a lot of their new high speed routes are much longer than we're building, and not really for routes that are already popular/at capacity with existing rail, China is building them for several reasons that include off the top of my head:
A way to keep/improve their capabilities for constructing rail networks and making trains.
Employ very large numbers of people as a way to keep money moving in their economy.
Looking ahead for the next 25-50 years - many of our rail routes took decades to really become popular/hit capacity.
National Prestige - Look we've built more high speed rail than anyone else, and done it in a fraction of the time, we're a great nation!.